Minimal Reversible Deterministic Finite Automata

Weakly and Strongly Irreversible Regular Languages

“…We point out that for k = 1, Theorem 1 gives a 2 n−1 upper bound, which matches with the bound for the conversion of DFAs into equivalent REV-DFAs, claimed in [3]. In the same paper, a lower bound very close to such an upper bound was presented.…”

“…The first works on this topic already appeared half a century ago and are due to Landauer and Bennet [9,2]. More recently, several papers presenting investigations on reversibility in space bounded Turing machines, finite automata, and other devices appeared in the literature (see, e.g., [1,15,6,10,13,3,11]).…”

“…In [3], the authors gave an automata characterization of the class of reversible languages, i.e., the class of regular languages which are accepted by reversible automata: a language is reversible if and only if the minimum deterministic automaton accepting it does not contain a certain forbidden pattern. Furthermore, they provide a construction to transform a deterministic automaton not containing such forbidden pattern into an equivalent reversible automaton.…”

“…We point out that, according to the approach in [3], in this paper we refer to the classical model of deterministic automata, namely automata with a unique initial state, a set of final states, and deterministic transitions. Different approaches have been considered in the literature.…”

“…The notion of reversibility in [1] is introduced by considering deterministic devices with one initial state and one final state, while automata with a set of initial states, a set of final states and deterministic transitions have been considered in [15]. In particular, the notion of reversibility in [1] is more restrictive than the one studied in [3] and in this paper. Hence, also the notion of k-reversibility, introduced and studied here, is different from a notion of k-reversibility studied in [1].…”